If you go to the library, it might be a good idea to check for any trade directories, I get the feeling that Thomas Henry Wade only lived at the Aughton address for a short while.
Referring back to earlier postings, it would seem that Catherine is your main line and yet we don't have much information on her, when she married, who her children were etc.
Looking at Thomas, we have him with the family in 1841, occupation clerk, birthplace uncertain.
1851 Village, Walton on the Hill, Lancashire
Thomas H Wade Head M 34 Clerk East India Merchant Yorkshire Amley
Elizabeth Wife M 32 Lancashire Everton
Elizabeth daur 8 " "
John B son 4 " "
Caroline daur 1 " Walton
Elizabeth Lewis Neice Unm 15 House Servant " Liverpool
HO107; Piece: 2191; Folio: 52; Page: 24
1861 Walton Village, Lancashire
Thomas Henry Wade Head M 45 Agent to the Northern Assurance Co. Armley Yorkshire
Elizabeth Wife M 42 Lancashire Everton
Elizabeth daur Unm 17
John Bateson Wade Son Unm 14 Scholar
Caroline daur 11 Scholar Walton
Sarah Hughes Servant 23 Domestic Servant Manchester Lancashire
RG9; Piece: 2723; Folio: 11; Page: 16
1871 Church Road, Walton on the Hill, Lancashire
Thomas H Wade Head M 55 Clerk Armley Yorkshire
Elizabeth Wife M 52 Lancashire Everton
Elizabeth daur Unm 28
Caroline 21 Walton
John B son 24 Clerk
Jane Gaskell Servant 22 Domestic Servant Aughton
RG10; Piece: 3831; Folio: 42; Page: 76
It seems very coincidental that the servant was born in Aughton I was wondering if the premises in Aughton that Thomas Henry had in 1879 could have been an office rather than residential.
1881 36 Derby Road, North Meols, Southport, Lancashire
Thomas H Wade Head Widr 65 Retired Commercial Clerk Yorkshire Armley
John B son Mar 33 Surveyors Clerk Lancashire Everton
Harriett Anderson Servant 17 General Servant Lancashire Westhead
RG11; Piece: 3749; Folio: 103; Page: 5